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In this paper, a GaN HEMT high efficiency amplifier and a module composed of a GaN HEMT amplifier are presented, which operates at 5.8GHz. GaN HEMT is considered to be suitable for harmonic tuned high efficiency amplifiers compared with existing GaAs FET amplifiers, due to its high voltage operation and high impedance natures. A high efficiency GaN HEMT amplifier is designed and evaluated, which is equipped with fundamental, second and third harmonic matching circuits in a hermetically sealed metal package. As a result, a high power added efficiency of 70.5% was obtained with associated output power of 7.3W. As the GaN HEMT employed in this work has already passed space qualify tests (SQT), this amplifier will be an important component to realize space solar power systems. Moreover, the module composed of this high efficiency GaN HEMT amplifier supplies the condition for the maximum performance of this amplifier. As a result, a high power added efficiency of 43+/-1% was obtained as a module.